Question

Product specifications call for a part at Vaidy Jayaraman's Metalworks to have a length of 1.000"±0.040". Currently, the process is performing at a grand average of 1.000 " with a standard deviation of 0.010 ". Is the process "capable"?

a.Yes
b. No

Answer 1

To determine if the process at Vaidy Jayaraman's Metalworks is "capable," we can calculate the process capability index (Cpk).

Step-by-step explanation:

The process at Vaidy Jayaraman's Metalworks is considered "capable" if it can consistently produce parts within the specified tolerance range. The tolerance range for the part's length is 1.000" ± 0.040". To determine if the process is "capable," we need to compare its performance to the tolerance range.

Given that the grand average length is 1.000" with a standard deviation of 0.010", we can calculate the process capability index (Cpk) to assess the process capability. Cpk is calculated using the formula:

Cpk = min((USL - μ) / (3σ), (μ - LSL) / (3σ))

Where:

• USL is the upper specification limit (1.04" in this case)
• μ is the grand average length (1.000" in this case)
• σ is the standard deviation of the process (0.010" in this case)
• LSL is the lower specification limit (0.96" in this case)

By substituting the values into the formula, we get:

Cpk = min((1.04 - 1.000) / (3×0.010), (1.000 - 0.96) / (3×0.010))